I thought that all ISOs value where pushed from 100 ISO.
Sort of. But there's analog gain prior to the conversion to digital (which is what 'native ISO range' means), and there's digital gain after ADC (expanded ISO settings). I believe that 'tweener' ISOs are also digital manipulations of analog gain applied in full-stop increments.
This is how it is easier to understand (in reality it is more complex)
1. Signal from sensor needs to be amplified because it is too weak to go straight to the A/D converter. There is a base "best" amplification factor at which the signal achieved after amplification will have the best signal to noise ratio preserving still the usable information. This would be the amplification (gain) required to get base ISO - let's say 100.
2. The amplified signal goes to the A/D converter which change analog electric signal (it's voltage) to the digital domain (numbers). They work simple - if you have an electric signal from 0V to (let's say max) 2V and you assume, that 0V is black and 2V is white (in terms of luminocity) and you want to get 16 bits resolution then you have 1 of 65536 different values representing the electric signal in the moment of sampling. Of course you need to have luminocity of pixels of different colors (RGB or even RGGB to get a color value). So in terms of image it would be luminocity value (shade of grey) of a single pixel. Imagine that electric signal from sensor is constructed by getting values from each pixel one by one.
3. If the signal is too weak it needs to be amplified stronger (like getting louder music). If you don't amplify it, then after A/D conversion you could get numbers only from the range let's say 0 to 10000. By amplifying weak signal you loose some information and introduce additional noise. There is a noise in the unamplified signal so by amplifying the signal you also make the noise more relevant. This is where dynamic range falls down and noise rises up.
4. Amplified and digitized signal represents the color values of the sensor's matrix. Digitized signal means that it's represented by values - from 0 to 65535 (in 16 bit resolution domain). If we have 14 bits resolution domain, then we have 16384 possible values for each pixel (in reality multiplied by three as there are 3 colors but here he talk about luminocity value of a single color value).
5. Let's say, that amplification gain required to achieve ISO 100 is equal to 5. Let's say, that gain required to achieve ISO 200 is equal 10 (this is just for this example). So it means, that if you could amplify the analog signal (before digital conversion) by 7.5, it would be equal to ISO 150.
6. But if you first get digital numbers at ISO 100 and later after A/D conversion multiply the achieved values by 1.5, you will get digital values "as if" they would be achieved with the analog gain equal to 7.5. This would be "pushing" ISO.
7. Same if you would divide digital values achieved at ISO 200 by ...(guess number
) you would get almost similar "values" like before - by applying analog gain equal 7.5 and it would be "pulling" ISO.
8. Why is it bad? Because in the amplified analog signal so also in converted signal, there can be values, which after the digital arithmetics would go beyond the scale (you cut off highlights so the become simply white) or they become more compressed at lower scale areas (so you compress shades and get banding) Why banding? Because if you have values 10 and 11 representing luminocity of pixels in a row you don't see banding. But if you divide 10 by 2 you get 5. If you divide 11 by 2 you get 5.5 which rounded down also gives you 5. This two pixels after digital arithmetics become the same.
Well... Short answers are better. I think I have described this quite good enough for simple imagination. In reality there are more tricks and it doesn't look quite like described above. I hope it helps to understand the process.
Edit: changed D/A to A/D :-)